Mathematics: a rectangle has 6 feet what are all the possible dimensions of the rectangle

a rectangle has 6 feet what are all the possible, №13491162, 16.01.2020 18:41

Mathematics

The perimeter of a parallelogram must be no less than 40 feet. the length of the rectangle is 6 feet. what are the possible measurements of the width? write an inequality to represent this problem. use w to represent the width of the parallelogram. [hint: the formula for finding the perimeter of a parallelogram is p = 2l + 2w. what is the smallest possible measurement of the width? justify your answer by showing all your work.

Step-by-step answer

P Answered by Master

The inequality representing the problem is $2l+2w\geq 40$ .

The smallest possible width should be at least 14 feet.

Step-by-step explanation:

Given;

Perimeter $(P)\geq 40\ ft$

Length of rectangle (l) = 6 feet

We need to find width of the rectangle.

Let the width of the rectangle be 'w'.

Now given as hint;

Perimeter P= 2l+2w

Therefore from given details we can say that

$2l+2w\geq 40$

Hence The inequality representing the problem is $2l+2w\geq 40$ .

Now Substituting the value of length we get;

$2\times 6 +2w\geq 40\\\\12+2w\geq 40$

Subtracting both side by 12 using Subtraction property of Inequality we get;

$12+2w-12\geq 40-12\\\\2w\geq 28$

Now By Using Division property of Inequality we get;

$\frac{2w}{2}\geq \frac{28}{2}\\\\w\geq 14\ ft$

Hence The smallest possible width should be at least 14 feet.

Mathematics

The perimeter of a parallelogram must be no less than 40 feet. The length of the rectangle is 6 feet. What are the possible measurements of the width? Write an inequality to represent this problem. Use w to represent the width of the parallelogram. [Hint: The formula for finding the perimeter of a parallelogram is What is the smallest possible measurement of the width? Justify your answer by showing all your work.

Step-by-step answer

P Answered by PhD

2

see below

Step-by-step explanation:

If you know that your perimeter must be no less than 40 feet, you can say that P >= 40 ft. Since P is given by P=2l+2w, you can combine the two equations into a single inequality:

2l+2w >= 40

If the length is given by 6 feet, then you can further simplify the inequality to be

12+2w >= 40 --> w >=14

This means that the smallest possible measurement of the width is 14 feet.

Mathematics

The perimeter of a parallelogram must be no less than 40 feet. The length of the rectangle is 6 feet. What are the possible measurements of the width? Write an inequality to represent this problem. Use w to represent the width of the parallelogram. [Hint: The formula for finding the perimeter of a parallelogram is P = 2 l + 2 w . What is the smallest possible measurement of the width? Justify your answer by showing all your work.

Step-by-step answer

P Answered by Specialist

$14\ ft$

Step-by-step explanation:

Given

Length of rectangle is $6\ ft$

Perimeter must be greater than 40 ft

Suppose l and w be the length and width of the rectangle

$\Rightarrow \text{Perimeter P=}2(l+w)\\\Rightarrow P\geq 40\\\Rightarrow 2(l+w)\geq40\\\Rightarrow l+w\geq20\\\Rightarrow w\geq20-6\\\Rightarrow w\geq14\ ft$

So, the smallest width can be $14\ ft$

Mathematics

The perimeter of a parallelogram must be no less than 40 feet. The length of the rectangle is 6 feet. What are the possible measurements of the width? Write an inequality to represent this problem. Use w to represent the width of the parallelogram. [Hint: The formula for finding the perimeter of a parallelogram is What is the smallest possible measurement of the width? Justify your answer by showing all your work.

Step-by-step answer

P Answered by Master

5

A. 2l + 2w > 40

B. 14 = w

Step-by-step explanation:

B. 40 = ( 2/6) + 2w

40 = 12 +2w

subtracted by

28 = 2w

and that equals

14= w

Mathematics

The perimeter of a parallelogram must be no less than 40 feet. the length of the rectangle is 6 feet. what are the possible measurements of the width? write an inequality to represent this problem. use w to represent the width of the parallelogram. [hint: the formula for finding the perimeter of a parallelogram is p = 2l + 2w. what is the smallest possible measurement of the width? justify your answer by showing all your work.

Step-by-step answer

P Answered by Master

The inequality representing the problem is $2l+2w\geq 40$ .

The smallest possible width should be at least 14 feet.

Step-by-step explanation:

Given;

Perimeter $(P)\geq 40\ ft$

Length of rectangle (l) = 6 feet

We need to find width of the rectangle.

Let the width of the rectangle be 'w'.

Now given as hint;

Perimeter P= 2l+2w

Therefore from given details we can say that

$2l+2w\geq 40$

Hence The inequality representing the problem is $2l+2w\geq 40$ .

Now Substituting the value of length we get;

$2\times 6 +2w\geq 40\\\\12+2w\geq 40$

Subtracting both side by 12 using Subtraction property of Inequality we get;

$12+2w-12\geq 40-12\\\\2w\geq 28$

Now By Using Division property of Inequality we get;

$\frac{2w}{2}\geq \frac{28}{2}\\\\w\geq 14\ ft$

Hence The smallest possible width should be at least 14 feet.

Mathematics

The perimeter of a parallelogram must be no less than 40 feet. the length of the rectangle is 6 feet. what are the possible measurements of the width? write an inequality to represent this problem. use w to represent the width of the parallelogram. [hint: the formula for finding the perimeter of a parallelogram is p = 2l + 2w. what is the smallest possible measurement of the width? justify your answer by showing all your work.

Step-by-step answer

P Answered by PhD

41

12 + 2w > 40

w > 19

Minimum value of w is 20 feet.

Step-by-step explanation:

If l is the length of the parallelogram and w is its width then the perimeter of the parallelogram will be given by P = 2l + 2w.

Now, given that l = 6 feet and P > 40 feet.

Hence, 2(6) + 2w > 40

⇒ 12 + 2w > 40

This is the required inequality.

Now, 2w > 38

⇒ w > 19 feet.

This is the measure of width (w) of the parallelogram.

Now, the smallest possible measurement of the width is 20 feet. (Answer)

Mathematics

The perimeter of a parallelogram must be no less than 40 feet. the length of the rectangle is 6 feet. what are the possible measurements of the width? write an inequality to represent this problem. use w to represent the width of the parallelogram. [hint: the formula for finding the perimeter of a parallelogram is p = 2l + 2w. what is the smallest possible measurement of the width? justify your answer by showing all your work.

Step-by-step answer

P Answered by Master

[tex]w\geq 14[/tex]

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

[tex]2l+2w\geq 40[/tex]

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

[tex]2\times 6+2w\geq 40[/tex]

now, we can solve for w

[tex]12+2w\geq 40[/tex]

subtract both sides by 12

[tex]12+2w-12\geq 40-12[/tex]

[tex]2w\geq 28[/tex]

divide both sides by 2

and we get

[tex]w\geq 14[/tex]

so,

the smallest possible measurement of the width is 14 feet

Mathematics

The perimeter of a parallelogram must be no less than 40 feet. the length of the rectangle is 6 feet. what are the possible measurements of the width? write an inequality to represent this problem. use w to represent the width of the parallelogram. [hint: the formula for finding the perimeter of a parallelogram is p = 2l + 2w. what is the smallest possible measurement of the width? justify your answer by showing all your work.

Step-by-step answer

P Answered by Specialist

[tex]w\geq 14[/tex]

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

[tex]2l+2w\geq 40[/tex]

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

[tex]2\times 6+2w\geq 40[/tex]

now, we can solve for w

[tex]12+2w\geq 40[/tex]

subtract both sides by 12

[tex]12+2w-12\geq 40-12[/tex]

[tex]2w\geq 28[/tex]

divide both sides by 2

and we get

[tex]w\geq 14[/tex]

so,

the smallest possible measurement of the width is 14 feet

Mathematics

/// worth 70 points /// asap 3. a community is developing plans for a pool and hot tub. the community plans to form a swim team, so the pool must be built to certain dimensions. answer the questions to identify possible dimensions of the deck around the pool and hot tub. part i: the dimensions of the pool are to be 25 yards by 9 yards. the deck will be the same width on all sides of the pool. including the deck, the total pool area has a length of (x + 25) yards, and a width of (x + 9) yards. write an equation representing the total area of the

Step-by-step answer

P Answered by PhD

131

A community is developing plans for a pool and hot tub. The community plans to form a swim team, so the pool must be built to certain dimensions. Answer the questions to identify possible dimensions of the deck around the pool and hot tub.

Part I: The dimensions of the pool are to be 25 yards by 9 yards. The deck will be the same width on all sides of the pool. Including the deck, the total pool area has a length of (x + 25) yards, and a width of (x + 9) yards.

Write an equation representing the total area of the pool and the pool deck. Use y to represent the total area. Hint: The area of a rectangle is length times width. (1 point)

y = (x+25)(x+9)

Rewrite the area equation in standard form. Hint: Use the FOIL method. (1 point)

y = x^2 + 9x + 25x + 9(25)

y = x^2 +34x + 225

Rewrite the equation from Part b in vertex form by completing the square. Hint: Move the constant to the other side, add to each side, rewrite the right side as a perfect square trinomial, and finally, isolate y. (4 points: 1 point for each step in the hint)

y-225 = x^2 +34x

y-225 + 17^2 = x^2 +34x + 17^2

y-225 + 289 = (x+17)^2

y = (x+17)^2 - 64

What is the vertex of the parabola? What are the x- and y-intercepts? Hint: Use your answer from Part a to identify the x-intercepts. Use your answer from Part b to identify the y-intercept. Use your answer from Part c to identify the vertex. (4 points: 1 point for each coordinate point)

The vertex is where the squared term is zero, x=-17 , y =-64, (-17,-64)

The y intercept is y at x=0, so (0,225)

The x intercepts are the zeros; so at x=-25 and x=-9, aka (-25,0), (-9,0)

Graph the parabola. Use the key features of the graph that you identified in Part d. (3 points)

[Plot the points we generated and connect the dots. I'll leave the graphing to you]

In this problem, only positive values of x make sense. Why? (1 point)

x is the width of the pool edge; it must be positive.

What point on your graph shows a total area that includes the pool but not the pool deck? (1 point)

x=0, y=225 i.e. (0,225)

The community decided on a pool area that adds 6 yards of pool deck to both the length and the width of the pool. What is the total area of the pool and deck when x = 6 yards? (2 points)

(9+6)(25+6)=15(31)=465

Part II: A square hot tub will be placed in the center of an enclosed area near the pool. Each side of the hot tub measures 6 feet. It will be surrounded by x feet of deck on each side. The enclosed space is also square and has an area of 169 square feet. Find the width of the deck space around the hot tub, x.

Step 1: Write an equation for the area of the enclosed space in the form y = (side length)2. Hint: Don't forget to add x to each side of the hot tub. (1 point)

y=(x+6)(x+6)=(x+6)^2

Step 2: Substitute the area of the enclosed space for y in your equation. (1 point)

169 = (x+6)^2

Step 3: Solve your equation from Part b for x. (3 points)

$x + 6 = \pm \sqrt{169}$

$x = -6
 \pm 13$

$x= 7 \quad \textrm{ or } \quad x= -19$

Step 4: What is the width of the deck around the hot tub? Hint: One of the answers from Part c is not reasonable. (1 point)

Only the positive root works,

x=7 feet

Mathematics

/// worth 70 points /// asap 3. a community is developing plans for a pool and hot tub. the community plans to form a swim team, so the pool must be built to certain dimensions. answer the questions to identify possible dimensions of the deck around the pool and hot tub. part i: the dimensions of the pool are to be 25 yards by 9 yards. the deck will be the same width on all sides of the pool. including the deck, the total pool area has a length of (x + 25) yards, and a width of (x + 9) yards. write an equation representing the total area of the

Step-by-step answer

P Answered by PhD

131

A community is developing plans for a pool and hot tub. The community plans to form a swim team, so the pool must be built to certain dimensions. Answer the questions to identify possible dimensions of the deck around the pool and hot tub.

Part I: The dimensions of the pool are to be 25 yards by 9 yards. The deck will be the same width on all sides of the pool. Including the deck, the total pool area has a length of (x + 25) yards, and a width of (x + 9) yards.

Write an equation representing the total area of the pool and the pool deck. Use y to represent the total area. Hint: The area of a rectangle is length times width. (1 point)

y = (x+25)(x+9)

Rewrite the area equation in standard form. Hint: Use the FOIL method. (1 point)

y = x^2 + 9x + 25x + 9(25)

y = x^2 +34x + 225

Rewrite the equation from Part b in vertex form by completing the square. Hint: Move the constant to the other side, add to each side, rewrite the right side as a perfect square trinomial, and finally, isolate y. (4 points: 1 point for each step in the hint)

y-225 = x^2 +34x

y-225 + 17^2 = x^2 +34x + 17^2

y-225 + 289 = (x+17)^2

y = (x+17)^2 - 64

What is the vertex of the parabola? What are the x- and y-intercepts? Hint: Use your answer from Part a to identify the x-intercepts. Use your answer from Part b to identify the y-intercept. Use your answer from Part c to identify the vertex. (4 points: 1 point for each coordinate point)

The vertex is where the squared term is zero, x=-17 , y =-64, (-17,-64)

The y intercept is y at x=0, so (0,225)

The x intercepts are the zeros; so at x=-25 and x=-9, aka (-25,0), (-9,0)

Graph the parabola. Use the key features of the graph that you identified in Part d. (3 points)

[Plot the points we generated and connect the dots. I'll leave the graphing to you]

In this problem, only positive values of x make sense. Why? (1 point)

x is the width of the pool edge; it must be positive.

What point on your graph shows a total area that includes the pool but not the pool deck? (1 point)

x=0, y=225 i.e. (0,225)

The community decided on a pool area that adds 6 yards of pool deck to both the length and the width of the pool. What is the total area of the pool and deck when x = 6 yards? (2 points)

(9+6)(25+6)=15(31)=465

Part II: A square hot tub will be placed in the center of an enclosed area near the pool. Each side of the hot tub measures 6 feet. It will be surrounded by x feet of deck on each side. The enclosed space is also square and has an area of 169 square feet. Find the width of the deck space around the hot tub, x.

Step 1: Write an equation for the area of the enclosed space in the form y = (side length)2. Hint: Don't forget to add x to each side of the hot tub. (1 point)

y=(x+6)(x+6)=(x+6)^2

Step 2: Substitute the area of the enclosed space for y in your equation. (1 point)

169 = (x+6)^2

Step 3: Solve your equation from Part b for x. (3 points)

$x + 6 = \pm \sqrt{169}$

$x = -6
 \pm 13$

$x= 7 \quad \textrm{ or } \quad x= -19$

Step 4: What is the width of the deck around the hot tub? Hint: One of the answers from Part c is not reasonable. (1 point)

Only the positive root works,

x=7 feet

a rectangle has 6 feet what are all the possible dimensions of the rectangle

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